The Scot saw his side fall to defeat in Tuesday's semi-final first leg at the Stadium of Light, despite naming a strong side for the encounter.
United looked to have claimed a draw when Nemanja Vidic's second-half header cancelled out Ryan Giggs' own goal in the opening period.
Sunderland, however, restored their lead through Fabio Borini's thunderous penalty after Adam Johnson had tumbled in the area under a challenge from Tom Cleverley.
The visitors piled on the pressure in the closing stages, but Gus Poyet's men stood firm to make it three defeats in a row in all competitions for United.
Moyes was incensed after the final whistle, believing there had been no foul on Steven Fletcher for the free-kick that led to the opening goal, while also questioning referee Andre Marriner's penalty decision.
And the former Everton manager feels United are competing against both their opponents and match officials at present.
"I thought the referee was going to blow in our direction for the first goal," he told Sky Sports. "I couldn't believe he gave a free-kick. It was a terrible decision."
On the penalty call, he added: "We are all just laughing at them (officials) at the minute. We get a player booked for doing the same thing (going down easily).
"It looks as though we are having to play them (officials) as well as the opposition at the moment."
United can still reach the final if they can overcome the deficit in the return leg at Old Trafford on January 22 - and Moyes is relishing the challenge.
"It is difficult we just need to keep going. We didn't do a lot wrong," he continued. "I thought the players, our crowd were unbelievable, the players deserved to get a result.
"It's a two-legged game and I am really looking forward to the second leg."
